In a gas turbine a plurality of stationary stator or guide vanes are used which are arranged in rows along the circumference of the turbine portion. As these stator vanes are subjected to the effects of the hot gases flowing out of the combustion chamber and of the high pressures, high stresses can arise in the stator vanes and the platforms. The platform is situated between the hot gas flow and space filled with cooling air. In order to seal this space from the hot gases the platform usually has side walls which are provided with a groove extending in the longitudinal direction of the platform. The grooves of two neighboring platforms (in the circumferential direction) receive a sealing plate extending between the two platforms. In some cases the distance, in the circumferential direction of the gas turbine, between the trailing edge of the stator vane and the groove can be very small. This can lead to considerable stress concentrations, particularly in the trailing edge of the stator vane and in the platform in the area of the trailing edge of the stator vane. Because of these stress concentrations the life time of the stator vane is significantly reduced.